J. Phys. Chem. B 1998, 102, 9461-9472
9461
Monolayers of Hexadecyltrimethylammonium p-Tosylate at the Air-Water Interface. 1. Sum-Frequency Spectroscopy G. R. Bell, Z. X. Li, and C. D. Bain* Physical and Theoretical Chemistry Laboratory, UniVersity of Oxford, South Parks Road, Oxford, OX1 3QZ, United Kingdom
P. Fischer and D. C. Duffy Department of Chemistry, UniVersity of Cambridge, Lensfield Road, Cambridge, CB2 1EW, United Kingdom ReceiVed: May 6, 1998; In Final Form: July 28, 1998
Sum-frequency vibrational spectroscopy has been used to determine the structure of monolayers of the cationic surfactant, hexadecyltrimethylammonium p-tosylate (C16TA+Ts-), at the surface of water. Selective deuteration of the cation or the anion allowed the separate detection of sum-frequency spectra of the surfactant and of counterions that are bound to the monolayer. The p-tosylate ions are oriented with their methyl groups pointing away from the aqueous subphase and with the C2 axis tilted, on average, by 30-40° from the surface normal. The vibrational spectra of C16TA+ indicate that the number of gauche defects in the monolayer does not change dramatically when bromide counterions are replaced by p-tosylate. The ends of the hydrocarbon chains of C16TA+ are, however, tilted much further from the surface normal in the presence of p-tosylate than in the presence of bromide. A quantitative analysis of the sum-frequency spectra requires a knowledge of the molecular hyperpolarizability tensor: the role of ab initio calculations and Raman spectroscopy in determining the components of this tensor is discussed.
1. Introduction When charged surfactants form micelles, charge neutrality requires that an equal number of oppositely charged ions are associated with the micelle.1 These counterions can reside benignly in the diffuse part of the electrical double layer or can interact specifically with the surfactant molecules. These specific interactions have a profound effect on the geometry of the aggregate and on physical properties of surfactant solutions. Much experimental and theoretical work has been carried out to understand these effects,2-4 but the interactions that control them are still poorly understood. The intermolecular forces that exist between counterions and micelles in solution also operate in monolayers of surfactants at the air-water interface. Monolayers can provide structural information that is difficult to obtain from micelles. The surface of water provides a reference plane and the surface normal a reference direction from which the location and orientation of the surfactant and counterion can be measured. Randomly oriented micelles present no such convenient references, and shear forces or magnetic anisotropy has to be exploited to induce some degree of orientation into the aggregates. The study of monolayers does, however, require specialized surface-sensitive techniques. Here we present the results of two such techniques, sum-frequency spectroscopy (SFS) and neutron reflection (NR), applied to a monolayer of a cationic surfactant, hexadecyltrimethylammonium p-tosylate (C16TA+Ts-), adsorbed at the air-water interface. In the first of two papers, we present vibrational spectra of the monolayer obtained by infrared-visible sum-frequency generation and discuss the interpretation of the spectra in terms of the structure of the monolayer. In the accompanying paper, we present * Corresponding author. E-mail
[email protected].
results obtained by neutron reflection and discuss the relevance of the structure of the monolayer to aggregation in bulk solution.5 A preliminary communication summarizing the main structural features of the monolayer has been published previously.6 The larger part of these two papers is devoted to a detailed analysis of the experimental data. To help readers follow the arguments, we provide a brief summary of the final conclusions here. The addition of p-tosylate to a solution of C16TAB increases the area per surfactant molecule by 25%, in contrast to the normal affect of salt, which is to decrease the area per molecule. Eighty percent of the tosylate counterions are bound to the monolayer; the remaining 20% are presumed to lie in the diffuse double layer. The tosylate ions lie deep within the hydrophobic region of the monolayer: the center of the distribution of the tosylate ions is coplanar with the sixth methylene unit of the hydrocarbon chain, counting from the polar end. The counterions are tilted, on average, 30-40° from the surface normal with the hydrophobic part of the ions oriented away from the water. Addition of p-tosylate results in an increase in the tilt of the outermost part of the hydrocarbon chain of the surfactant, consistent with the maintenance of a liquidlike density in the monolayer. In bulk solutions, addition of p-tosylate causes a sphere-to-rod transition in the micellar geometry. In the following paper, we show how the structure of the monolayer can be used to rationalize this transition within a simple geometric model of micellar aggregation. SFS is a form of nonlinear optical spectroscopy that provides vibrational spectra of molecules in noncentrosymmetric environments.7 SFS is only sensitive to molecules at interfaces where the centrosymmetry of isotropic bulk phases is broken. Sumfrequency (SF) spectra not only provide a characteristic
10.1021/jp982142+ CCC: $15.00 © 1998 American Chemical Society Published on Web 10/30/1998
9462 J. Phys. Chem. B, Vol. 102, No. 47, 1998 “fingerprint” of the molecules at the surface but also contain intrinsic information on the surface structure. Analysis of SF spectra yields the polar orientation and tilt of molecules adsorbed at surfaces.7 Interpretation of the C-H stretching modes in the SF spectra of long hydrocarbon chains has been especially fruitful in determining the conformational order in surfactant monolayers.8,9 Both aromatic counterions and surfactant monolayers have vibrational modes that are SF-active. We have previously used SFS to study the binding of counterions to surfactant monolayers at the solid-water interface.10-13 Initial experiments were performed on the pseudohalides, thiocyanate (SCN-)10 and cyanide (CN-),12,13 coadsorbed with the tetradecyltrimethylammonium ion (C14TA+) at a hydrophobic surface. The C-N stretching modes in the SF spectra showed that both the SCNand CN- ions were bound to the monolayer with the nitrogen atom furthest from the solid substrate. This study was extended to three aromatic counterions: p-tosylate, benzoate, and salicylate.11 All three counterions were bound to the monolayer with their aromatic rings oriented away from the aqueous phase. In the one previous study of counterion binding to surfactant monolayers at the air-water interface, we showed that benzoate ions bound to a monolayer of C14TA+ were oriented close to the surface normal.14 In neutron reflection, the reflectivity of a neutron beam is measured as a function of momentum transfer perpendicular to the surface of water.15 Reflectivity curves depend on the scattering amplitudes and densities of the molecules at the surface and can be analyzed to yield the area per molecule and the thickness of the film.16 NR has been applied extensively in the study of surfactants adsorbed at the air-water interface.15-17 Since hydrogen and deuterium atoms scatter neutrons out of phase with each other, a mixture of H2O and D2O can be produced in which the scattering from the hydrogen atoms exactly cancels the scattering from O and D. Neutrons are not reflected from the interface between air and such a mixture: this mixture is referred to as null-reflecting water (nrw). Deuterated surfactants scatter neutrons strongly and can be detected readily at the surface of nrw. Since coherent scattering from protonated surfactants is weak, selective deuteration of the surfactant and its counterion allows the surface coverage of each to be measured independently. More complex experiments involving partial deuteration yield the relative locations of the counterion and surfactant molecules.5 The salts of C16TA+ have a rich solution chemistry that has been the subject of extensive studies. C16TA+ is a single-chain cationic surfactant that forms small (∼50 Å diameter) spherical micelles above the critical micellar concentration (cmc) in the presence of simple inorganic ions such as bromide. At high concentrations, or in the presence of large amounts of salt ([NaBr] > 0.1 M), elongated, rod-shaped micelles are observed.18 The sphere-to-rod transition at high ionic strength is ascribed to a reduction in repulsions between the cationic headgroups due to electrostatic screening by counterions. This transition is observed with most (but not all) inorganic ions: counterions that interact very weakly with the surfactant (e.g., Cl-) are ineffective in screening the repulsions between the headgroups. Some aromatic anions can induce a sphere-to-rod transition at much lower concentrations (∼1 mM). The first example, the salicylate ion, was discovered more than 20 years ago2 and has been studied extensively since.3 Many other cationic surfactant-counterion combinations have been identified that form rod-shaped aggregates at low concentrations,4 including the system we study here: C16TAB + p-tosylate.19
Bell et al. The transition from small spherical micelles to aggregates with rodlike structures can have a remarkable effect on the rheological and optical properties of the surfactant solution.2-4,19,20 For example, a solution of C16TAB at its cmc has a low viscosity and is optically isotropic. In the presence of 2 mM sodium salicylate, the solution becomes highly viscous, and trapped air bubbles are seen to recoil, indicating that the solution has elastic properties. The solution is also optically birefringent under shear.3 Cylindrical micelles exist in solutions of C16TAB + p-tosylate at an anion concentration of 1 mM, and viscoelastic properties are observed at higher concentrations (20 mM). The solutions also display flow birefringence.19 These unusual properties arise from interactions between elongated micelles.4 For example, viscoelasticity occurs when the micelles reach a critical length, become entangled, and can no longer flow easily past one another; flow birefringence and iridescence arise from alignment of the micelles.4 These surfactant systems show many similarities to polymer solutions in the semidilute regime.21 One of the intriguing features of these properties is the sensitivity to subtle differences in the molecular structure of counterions. For example, solutions of C16TAB become viscoelastic if p-dichlorobenzoate is added, while o-dichlorobenzoate has no effect.2 Conversely, o-hydroxybenzoate (salicylate) causes viscoelasticity but p-hydroxybenzoate does not.2,22 Several techniques provide information on the molecular structure of these surfactant aggregates. Light scattering23 and small-angle neutron scattering (SANS)24 yield the size, geometry, and number of surfactant molecules in the aggregate. Cryotransmission electron microscopy provides direct images of entangled rodlike structures.4a,25 Low-angle X-ray diffraction (XRD) has been used to study the long-range order of these aggregates in solution.26 1H and 13C NMR are particularly informative:27-31 the polarity of the environment alters the 13C chemical shifts in the aromatic anions, and the ring current of the benzene ring changes the chemical shift of protons in the hydrocarbon chains of the surfactant that are near the ring. The 13C chemical shifts indicate that the benzene rings of many aromatic anions reside in a region less polar than water, presumably within the micelle. From the relative chemical shifts of the ortho, meta, and para protons, some workers have attempted to determine the average orientation of the counterions.27-29 The C16TAB + p-tosylate system we study here has been characterized previously in the bulk phase by fluorescence,32 FTIR, XRD, microscopy, and NMR.19 NMR studies have stimulated debate on the relationship between the ability of a counterion to induce sphere-to-rod transitions and the orientation and position of the counterion within the aggregate. Iyer et al.28 asserted that viscoelasticity was correlated with the orientation of the counterions. Their observations indicated that hydroxybenzoate counterions with their COO- group oriented perpendicular to the micellar surface induced viscoelasticity, whereas counterions with the COOgroup oriented parallel to the surface did not. Bachofer demurred and provided the counterexample of o-toluate anions, which do not induce viscoelastic behavior but have their COOgroups oriented perpendicular to the surface.29a Bachofer preferred a geometric model proposed by Israelachvili et al.,33 in which the structure of a surfactant aggregate is determined by V/al, where V is the volume of the hydrocarbon tail, a is the effective area of the charged headgroup, and l is the maximum effective length of the hydrocarbon chain. For values of V/al < 1/3, the formation of structures with high curvature, such as spheres, is favored; higher values of V/al result in the formation of structures with lower curvature such as rods and sheets. The
C16TA+Ts- at the Air-Frequency Interface
J. Phys. Chem. B, Vol. 102, No. 47, 1998 9463 the nonlinear response of the substrate. χ(2) ijk,R is a macroscopic property of the interface and is related to the microscopic hyperpolarizability, βlmn, of the individual molecules in the interface averaged over all their orientations:
χ(2) ijk,R ) f
Figure 1. (A) Geometry of the SF experiment. The Cartesian axes of the surface are shown. (B) Definition of Euler angles used in text.
influence of counterions is then rationalized in terms of changes in V and a. Magid reached a similar conclusion from an NMR study of dichlorobenzoates bound to C16TAB micelles.27 She found that aromatic anions that induced viscoelasticity penetrated more deeply into the micellar core than anions that did not. Smith et al.22 suggested that only those ions in which both the hydrophobic and hydrophilic groups can reside in their preferred environments promote sphere-to-rod transitions. Despite this large number of studies, the molecular interactions that control sphere-to-rod transitions are not fully understood. 2. Sum-Frequency Spectroscopy (SFS) In SFS, two pulsed laser beams, one in the visible (ωvis) and the other in mid-IR (ωIR), are overlapped at a surface, and the light emitted at the sum-frequency (ωsum ) ωvis + ωIR) is detected.7 The signal detected at the sum-frequency (Ssum) depends on the second-order nonlinear susceptibility of the surface, χ(2) ijk , and the intensities of the incident laser beams, Ivis and IIR. Within the electric dipole approximation, the signal (in photons per pulse) is given by34
Ssum ) 20Aτ cos θsumIvisIIR 2 | Li(ωsum)χ(2) ijk Kj(ωvis) Kk(ωIR)| , pωsumc ijk ijk ) xyz (1)
∑
Kj(ωvis) and Kk(ωIR) are the ratio of the electric fields at the surface to the electric fields in air; Li(ωsum) relates the polarization at the sum-frequency (SF) to the electric field of the emitted SF light in the bulk medium (in this case, air); A and τ are the spatial and temporal overlap of the laser beams at the surface; θsum is the angle between the wavevector of the emitted SF light and the surface normal, and xyz refer to the Cartesian surfacefixed axes. The experimental geometry is shown in Figure 1A. The susceptibility can be broken down into two parts: a resonant term, χ(2) ijk,R, arising from the vibrational modes of adsorbed molecules and a nonresonant term, χ(2) NR, arising from
N 〈β 〉, lmn ) abc 0 lmn
(2)
N is the number of the molecules per unit area, f relates the local electric field experienced by the molecules to the macroscopic electric field in the medium, and abc refer to the Cartesian molecular axes. χ(2) and β are third-rank tensors that change sign under inversion. In the bulk phase, the surfactant molecules are randomly oriented, and therefore the orientational average over β will vanish: the contribution from molecules with one orientation will be canceled by an equal number of molecules with the opposite orientation. The interface breaks the symmetry of the bulk phases. The different forces acting on the two sides of the interface generally result in a preferred orientation of molecules at the surface. The monolayers we consider here are azimuthally isotropic but are asymmetric in the direction normal to the surface. This asymmetry leads to nonzero values of χ(2) and hence to the emission of sumfrequency light.35 When the frequency of the IR laser is close to a molecular vibrational frequency, βlmn can be expressed in terms of the IR and Raman transition dipole moments, µ′n and R′lm36
βlmn )
R′lmµ′n 2p(ωv - ωIR - iΓv)
(3)
ωυ is the frequency of a vibrational mode, and Γυ is its homogeneous line width. When the IR laser is in resonance with an IR- and Raman-active vibrational mode of the molecules at the surface, χ(2) ijk,R increases. By scanning the frequency of the IR laser and detecting the intensity of the SF light, we can therefore obtain a vibrational spectrum of the adsorbed molecules. Interpretation of sum-frequency vibrational spectra is complicated by the fact that χ(2) generally contains contributions from several modes, ν, in addition to the nonresonant background from the substrate:
χ(2) ) χ(2) NR +
∑ν χ(2)ijk,R
(4)
Since the SF signal depends on |χ(2)|2, these contributions are convoluted with one another, and the resulting line shapes depend strongly on the relative phases and strengths of χ(2) ijk,R and χ(2) NR. The K and L terms in eq 1 can be collated into overall Fresnel factors, Fijk ) Li(ωsum) Kj(ωvis) Kk(ωIR). The SF signal can then be written as 2 Fijkχ(2) ∑ ijk | ijk
Ssum ) k′|
(5)
where k′ is a constant that depends on the lasers and the experimental geometry. For monolayers that are isotropic in the plane of the surface, there are only four independent (2) (2) (2) (2) (2) (2) (2) components of χ(2) ijk : χzzz, χxxz ) χyyz, χxzx ) χyzy, χzxx ) χzyy. If the frequencies of the SF and visible beams are far removed from electronic resonances in the molecules, then the Raman (2) 37 tensor is symmetric and χ(2) xzx ) χzxx.
9464 J. Phys. Chem. B, Vol. 102, No. 47, 1998
Bell et al. and the x-axis is randomly distributed since the surface is isotropic in the plane. We further assume that the distribution of angles ψ is isotropic, where ψ is the angle between the a-axis and the cz-plane; i.e., we assume that the twists of the molecules about the c-axis are random. The components of the transformation matrix can therefore be averaged over φ and ψ and are then solely a function of the tilt angle, θ, between the c-axis and the surface normal. It is this angle, θ, that we seek to determine from a quantitative analysis of the SF spectra. The modes we observe in p-tosylate have either A1 or B1 symmetry in the C2V point group that results from free rotation of the CH3 and SO3- groups. For the A1 modes, there are three nonzero components of the hyperpolarizability: βaac, βbbc, and βccc. Expressions that relate χ(2) to β for the symmetric methyl modes are given elsewhere;9 for the C-H stretching modes of the ring, we can ignore βbbc, and the resulting expressions for χ(2) are
χ(2) zzz )
Nf (〈cos θ〉 (6t + 1) - 〈cos 3θ〉 (1 - 2t))βaac 80
(7a)
χ(2) xxz )
Nf (〈cos θ〉(2t + 7) + 〈cos 3θ〉(1 - 2t))βaac 160
(7b)
χ(2) xzx )
Nf (〈cos θ〉(2t - 1) - 〈cos 3θ〉(1 - 2t))βaac 160
(7c)
where t ) βccc/βaac. For the B1 modes, Figure 2. Normal modes of p-tosylate observed in SF spectra. The labeling of the aromatic modes follows that of Wilson (ref 39). The lengths of the C-H bonds shown are proportional to the bond displacements of the modes calculated ab initio. The Cartesian axes of the p-tosylate molecule are shown.
Different components of χ(2) ijk can be probed with different polarizations of the electric fields at the interface. For monolayers that are azimuthally isotropic, only four combinations of polarization give rise to SF emission: ssp, sps, pss, and ppp, where the letters designate the polarizations of the SF, visible, and IR beams, respectively. The first three polarization combinations depend on a single component of χ(2), while the fourth combination contains an admixture of all four independent components:
Sssp ) k′|Fyyzχyyz|2
(6a)
Ssps ) k′|Fyzyχyzy|2
(6b)
Spss ) k′|Fzyyχzyy|2
(6c)
Sppp ) k′|Fzxxχzxx + Fxzxχxzx + Fxxzχxxz + Fzzzχzzz|2 (6d) If χyzy ) χzyy, sps- and pss-polarized spectra differ only in intensity through differences in the Fresnel coefficients. The susceptibilities are related to the molecular hyperpolarizability by a sixth-rank matrix of direction cosines, which have been tabulated by Hirose.38 The components of the transformation matrix depend on the Euler angles (θ,ψ,φ) relating the molecular and laboratory axis systems (Figure 1B). In this paper, we will be concerned with the interpretation of the CH3 symmetric stretching mode of the surfactant and the aliphatic and aromatic C-H stretching modes of the p-tosylate ion. The molecular axis systems are shown in Figure 2. The azimuthal angle, φ, between the projection of the c-axis in the xy-plane
χ(2) zzz )
Nf (〈cos θ〉 - 〈cos 3θ〉)βaca 40
(7d)
χ(2) xxz )
Nf (〈cos θ〉 - 〈cos 3θ〉)βaca 80
(7e)
Nf (3〈cos θ〉 + 〈cos 3θ〉)βaca 80
(7f)
χ(2) xzx )
To determine θ from experimental data, we generally need to know the components of the hyperpolarizability tensor which, in turn, implies a knowledge of the infrared and Raman transition dipole moments (eq 3). It is easier to work with ratios of susceptibilities, since then only the relative values of different components of β are required. The relative magnitudes of the components of the IR transition dipole moment can usually be estimated by symmetry or from IR spectra. The Raman tensor provides a greater challenge. Rarely are the individual components of the Raman tensor known experimentally. For some molecules a Raman depolarization ratio has been measured, but this ratio is only useful in the context of a Raman tensor with only two independent components, and even then ambiguities remain. Hyperpolarizabilities can also be calculated ab initio, but the computer time required to obtain quantitative results for large molecules remains prohibitive. The extent to which these problems can be resolved for different modes in p-tosylate is discussed in section 4. 3. Experimental Section The laser system in Oxford has been described in detail elsewhere.9 The IR laser beam (2800-3100 cm-1, 20 Hz, ∼1 ns, 1 mJ/pulse,
